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Suggested Adaptive Tools and Materials for Braille Students In Algebra and Geometry

Math Materials in Nemeth Code

Braille Algebra or Geometry Textbook with correct Nemeth Code and high quality tactile graphics. My last Braille geometry textbook (transcribed by a certified Nemeth transcriber) had several Nemeth Code errors and extremely poor quality tactile graphics throughout. The graphics had been entirely omitted or been drawn poorly. The poor quality was such that students were either unable to answer a question or give a correct answer. Both the VI and math teacher needs to be alert for such errors.

Nemeth Translation Software Package. This is necessary to produce materials (worksheets, reviews, tests, etc.) in Nemeth Code in a timely fashion for student use. Choose MegaMath or DBT in conjunction with Scientific Notebook from the following vendors:

Basic Tools or Technology

The student will need a Braillewriter, Refreshable Notetaker or Desktop Computer with Refreshable Braille Keyboard, Braille Paper, and a Braille Eraser. An Abacus is also strongly suggested.

Calculators

ORION TI-36X (Current price: $249) http://www.orbitresearch.com/
Your student may prefer a stand-alone talking scientific calculator, and although there are many such calculators on the market today, the ORION TI-36X from Orbit Research is currently the most affordable and user-friendly. While it does not have graphing capabilities, it is easily accessible by totally blind students (unlike the TI graphing calculators), and features a built-in learning mode. The ORION's LCD display and functionality are identical to the TI-36X, so math teachers should feel very comfortable orienting the visually impaired student. The ORION TI-36X replaces the ORION TI-34, which is now out of production. It is more powerful than the ORION TI-34 and costs $249. I evaluated the new model this past summer, made suggestions which they followed, and they are now available for purchase.

Sci-Plus Series 300 Scientific Calculator with Speech (Current price: Not Available) http://www.sightenhancement.com/
The Sci-Plus Series 300 is the only large display talking scientific calculator made as a one-piece portable unit. However, it does not have graphing capabilities. Sight Enhancement Systems manufactures it. Although most general education math teachers will be unfamiliar with the Sci-Plus, the various functions are easily identifiable, and a willing math teacher should have little difficulty orienting the visually impaired student to the Sci-Plus. This calculator is still in prototype, but it should be available to the general public soon. I'm not sure what the price will be, but I would suspect that the price will be more than the ORION TI-36X, but less than most of the other talking scientific calculator now available. I evaluated the prototype, and they are in the process of fixing the problems that I found.

Talking Scientific Graphing Calculator

Audio Graphing Calculator Version 2.0 (Current price: $295; Upgrade from 1.0 to 2.0: $145)
http://www.ViewPlus.com
The Audio Graphing Calculator (AGC) from ViewPlus Technologies, Inc. is a self-voicing graphing scientific calculator software program. Unlike a hand-held calculator, it displays results through speech and sounds, as well as visually presenting numbers and graphs. This program is intended to have capabilities comparable to a full-featured hand-held scientific and statistical graphing calculator. The AGC is truly accessible for all students, and could be used for the entire class. The onscreen graphics are easily seen by a low vision student via an enlargement feature, and the graph can be listened to by using the sophisticated audio wave feature. Print copies can be made with any standard printer using a variety of fonts, including braille. The print copies with braille fonts can be copied onto swell paper and run through a tactile imaging machine. One of the best ways to use the AGC is with a TIGER Braille/graphics embosser from ViewPlus Technologies, Inc., but the TIGER is rather expensive. Although considerable time is typically needed for training a blind student to use the ACG totally independently, the math teacher is usually able to assist the student because it is so user-friendly for the sighted individual.

Drawing/Construction Tools

Drawing Board . For constructions, my students don't use foil or the "usual" Sewell raised line drawing technique either. We use some type of rubber pad on a flat surface - whatever you have available. Some of my students and I happen to like an old Sewell raised line drawing board which has rubber attached to a clip board so that I can clip my Braille paper to this to keep it from sliding. But, others use a rubber pad on top of a regular wooden drawing board or table.

Recently, some tried using the Funky Foam Sheet from the 4 Kids Company. Still others might like a similar rubber on wood board from Howe Press because it too has a way of clipping the paper down.

Braille Compass from Howe Press. The compass has a regular pointed end, but the other end has a small tracing wheel attached. I have not been able to find these compasses anywhere else. Should you find another source, please let me know.

Straightedge - any "print" ruler will do if you don't have a plain straightedge, since the student is a Braille reader.

Tracing Wheel . Use one from the homemaking department, or Howe Press, or the APH tactile drawing kit, or the local hardware/hobby shop.

Braille/Print Protractor from APH is my preference. The student can draw an angle of a certain measure using the protractor and some sort of stylus or pen. I also wrote the teacher's guide.

Student-Generated Tactile Algebraic and Coordinate Geometry Graphics

Raised Line Graph Paper or The Graphic Aid for Mathematics from APH

Raised Line Graph Paper is available from APH. They have various sizes. You can get sheets measuring 8 1/2 x 11 inches or 11 1/2 x 11 inches. The squares can be 1/2-inch squares to 1-inch squares. Some have coordinate axes along with a grid pattern of horizontal and vertical lines. Unless you affix this graph paper to a corkboard as outlined below, you will need additional materials such as wikki stix to form the geometric figures.

The Graphic Aid for Mathematics is excellent for graphing algebraic equations, but can be used in geometry as well, especially coordinate geometry. It consists of a cork composition board mounted with a rubber mat, which has been embossed with a grid of 1/2-inch squares. My students use two rubber bands held down by thumbtacks for the x and y-axes. Then points are plotted with pushpins at the appropriate coordinates. Points are connected with rubber bands (for lines) or flat spring wires (for circles and arcs). Sighted math teachers can even interpret the student-made graphs correctly. You can also make your own rubber graph board by affixing a piece of raised line graph paper (also from APH) to a corkboard and proceeding as outlined above. The blind student can make this low tech tool high tech by taking a digital picture of each graph, which can be e-mailed to the math teacher.

Geometric Manipulatives

I am a firm believer in the use of manipulatives (for the sighted as well as the blind). The following manipulatives do not need to be adapted for the blind. I have accumulated mine over the years from various sources.

2-D Manipulatives are especially useful for teaching transformations (translations, reflections, and rotations) and similarity. I always have a box of triangles and quadrilaterals of different classifications close at hand and several regular polygons with five or more sides.

Paper Folding is extremely useful in teaching symmetry.

3-D Manipulatives are an absolute necessity when studying polyhedrons and other three-dimensional figures. In my experience, interpreting tactile 3-D drawings on a 2-D plane using perspective can sometimes be difficult for the average sighted person and thus more difficult for the low vision person. I have boxes of various 3-D solids including a tetrahedron, octahedron, hexahedron, dodecahedron, and icosahedron and right and oblique prisms, which are a little more difficult to find. A net is a pattern that can be cut out and folded into a three-dimensional figure (solid), and these can be either a great deal of fun or a matter of frustration for a low vision student depending on the student's spatial orientation abilities. However, some low vision students are even better able to conceptualize than their fully sighted counterparts.

Math Graphs Made by Others for Students

I recommend the following types of graphics:

Graphs Made by Using the Tactile Graphics Kit from APH. Region IV Education Service Center in Houston, TX has this down to an art (713-744-8144). Requires an artist, but well worth the effort for textbooks and standardized tests.

Graphs Made using a Tactile Imaging Machine (or "Toaster") and "Capsule" Paper: easy for mere mortals (I am no artist.), quick, and of especially high quality for geometric graphics.

"Capsule paper is a special paper onto which hundreds of millions of thermally-foamed microcapsules have been uniformly coated. These thermally foamed microcapsules have been developed for the purpose of stereo printing. While moving through the stereo copier, the capsule paper is irradiated with light energy and black portions of the copy absorb the energy and swell outward to form a stereo (raised line) copy." - taken from the description of "Matsumoto's Stereo Copying System for the blind."

We use different types of "capsule" paper at the Texas School for the Blind and Visually Impaired to make raised-line graphics. We have a Matsumoto's stereo copier from JP Trading because it was the first on the market. However, several other companies have since developed their own copiers and paper at a considerably lower price. The various "capsule" papers may be used interchangeably with different copiers; however, there is some variability in feel, durability, flexibility, cost, etc. We prefer the paper available from American Thermoform at the present time. Angles and figure markings made with the "toaster" method come out uniform, crisp, and tactually clear and concise.

Below is a list of three current sources of which I am aware and each company's specific name for their copier and paper:

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